Modelling non-stationary extremes of storm severity: a tale of two approaches

TL;DR

This paper introduces a unified framework combining parametric and semi-parametric models to better estimate non-stationary extreme storm events, optimizing bias-variance trade-offs and providing practical guidance for directional data analysis.

Contribution

It develops an iterative approach for modeling non-stationary extremes, integrating parametric and semi-parametric methods with automatic threshold estimation and bootstrap-based confidence bounds.

Findings

Unified framework for non-stationary extreme modeling

Application to North Sea storm wave data

Bootstrap confidence bounds for directional extremes

Abstract

Models for extreme values accommodating non-stationarity have been amply studied and evaluated from a parametric perspective. Whilst these models are flexible, in the sense that many parametrizations can be explored, they assume an asymptotic distribution as the proper fit to observations from the tail. This paper provides a holistic approach to the modelling of non-stationary extreme events by iterating between parametric and semi-parametric approaches, thus providing an automatic procedure to estimate a moving threshold with respect to a periodic covariate in circular data. By exploiting advantages and mitigating pitfalls of each approach, a unified framework is provided as the backbone for estimating extreme quantiles, including that of the $T$-year level and finite right endpoint, which seeks to optimize bias-variance trade-off. To this end, two tuning parameters related to the spread of peaks over threshold are introduced. We provide guidance for applying the methodology to the directional modelling of hindcast storm peak significant wave heights recorded in the North Sea. Although the theoretical underpinning for adaptation of well-known estimators in statistics of extremes to circular data is given in some detail, the derivation of their asymptotic properties lays beyond the scope of this paper. A bootstrap technique is implemented for obtaining direction-driven confidence bounds in such a way as to account for the relevant boundary restrictions with minimal sensitivity to initial point. This provides a template for other applications where the analysis of directional extremes is of importance.